The present invention relates to the field of wireless communication systems, in particular, intermodulation distortion (IMD) in multicarrier communication systems.
Interference is an undesirable result of increasingly crowded spectrum in modern communication systems. When multiple carriers share the same transponder high power amplifier (HPA), the transponder HPA may transmit a maximum signal strength when operating near a saturation output power level. However, operating near saturation will increase non-linearities in the HPA. Any non-linearity in the HPA may lead to IMD, which causes interference within a message itself as well as between the message signals by transferring modulations from one frequency range to another. The problem is particularly acute when cost effective nonlinearized HPA is operated with minimal output back-off. Output backoff (OBO) is the amount (in dB) by which the output power level of the HPA is reduced, or “backed-off,” from the saturation output power level. The problem is further compounded when the carriers passing through the HPA are bandwidth efficient, whose constellations include multiple concentric rings, and the carriers are tightly spaced within the limited spectrum.
IMD is the unwanted amplitude and phase modulation of signals containing two or more different frequencies in a system with nonlinearities. The intermodulation between each frequency component will form additional signals at frequencies that are not, in general, at harmonic frequencies (integer multiples) of either, but instead often at sum and difference frequencies of the original frequencies. The spurious signals, which are generated due to the nonlinearity of a system, are mathematically related to the original input signals. When the spurious signals are of sufficient amplitude, they can cause interference within the original system or in other systems, and, in extreme cases, loss of transmitted information, such as voice, data or video.
Broadband systems may be affected by all the nonlinear distortion products. Bandpass filtering can be an effective way to eliminate most of the undesired products without affecting in-band performance. However, third order intermodulation products are usually too close to the fundamental signals and cannot be easily filtered. The amplitude and phase distortion is unacceptable in systems that use higher order modulation schemes, because the distortion results in an error component in the received vector, degrading the receiver's bit error rate (BER).
FIG. 1 illustrates a conventional multicarrier communication system 100.
As illustrated in the figure, conventional multicarrier communication system 100 includes a plurality of transmitting sources and corresponding receiver front ends. Conventional multicarrier communication system 100 includes transmitting sources 102 and 104, however, there may be Mc independent carriers transmitting binary data. Additionally, conventional multicarrier communication system 100 includes receiver front ends 108 and 110, however, there may be Mc receiver front ends. Conventional multicarrier communication system 100 further includes an adder 136, a nonlinear transponder high power amplifier (HPA) 106 and an adder 138. Adder 138 models the additive white Gaussian noise i.e. AWGN. Adder 138 can be thought of as the channel, but is grouped in with HPA 106 for convenience.
Transmitting source 102 includes a bit source 112 a forward error correction (FEC) encoder 114, an interleaver 116, a gray-coded APSK modulator 118, a transmit filter 120 and a mixer 122. Transmitting source 104 includes a bit source 124, an FEC encoder 126, an interleaver 128, a gray-coded APSK modulator 130, a transmit filter 132 and a mixer 134.
Receiver frond-end 108 includes a mixer 140, a receive filter 142 and a sampling switch 144. Receiver frond-end 110 includes a mixer 146, a receive filter 148 and a sampling switch 150.
In FIG. 1, each of bit source 112, FEC encoder 114, interleaver 116, gray-coded APSK modulator 118, transmit filter 120, mixer 122, bit source 124, FEC encoder 126, interleaver 128, gray-coded APSK modulator 130, transmit filter 132, mixer 134, HPA 106, mixer 140, receive filter 142, sampling switch 144, mixer 146, receive filter 148 and sampling switch 150 are illustrated as distinct devices. However, at least two of bit source 112, FEC encoder 114, interleaver 116, gray-coded APSK modulator 118, transmit filter 120 and mixer 122 may be combined as a unitary device. Similarly, at least two of bit source 124, FEC encoder 126, interleaver 128, gray-coded APSK modulator 130, transmit filter 132 and mixer 134 may be combined as a unitary device. Similarly, at least two of mixer 140, receive filter 142, sampling switch 144 or one of mixer 146, receive filter 148 and sampling switch 150 may be combined as a unitary device.
Bit source 112 is operable to provide information data bits signal 152 for transmitting source 102 to FEC encoder 114. Non-limiting examples for bit source 112 include a source of data, images, video, audio, etc.
FEC encoder 114 is operable to receive information data bits signal 152 and provide encoded data bits signal 154 to interleaver 116. FEC encoder 114 provides forward error correction by adding redundancy to information data bits signal 152. Forward error correction improves the capacity of a channel by adding some carefully designed redundant information to the data being transmitted through the channel.
Interleaver 116 is operable to scramble the encoded data bits signal 154 by rearranging the bit sequence in order to make the distortion at the receiver more independent from bit to bit. Interleaving is a process of rearranging the ordering of a data sequence in a one to one deterministic format. Interleaving is used to enhance the error correcting capability of coding.
Gray-coded APSK modulator 118 is operable to modulate interleaved bits signal 156 to complex-valued data symbols 158, which follow two-dimensional constellation using Amplitude Phase Shift Keying (APSK). In this embodiment of multicarrier communication system 100 gray-coded APSK modulator is used, however, other modulation types may be used. For alphabet size M, complex-valued data symbols 158 generated by gray-coded APSK modulator 118 at the symbol rate of Ts−1 can be represented by {am,k; m=1, 2, . . . , Mc}k=−∞∞.
Transmit filter 120 is operable to convert complex-valued data symbols 158 to a waveform signal 160 using a pulse shaping function with an impulse response p1,T.
Mixer 122 is operable to mix waveform signal 160 with signal 162 to assign it an appropriate carrier frequency slot for transmitting. For transmitting source 102, signal 154 may be represented as ej(2πf1t+01)/√Mc.
For transmitting source 104, bit source 124, FEC encoder 126, interleaver 128 and gray-coded APSK modulator 130 operate in the similar manner as described above for transmitting source 102. However, transmit filter 132 is operable to generate a waveform signal 166 using a pulse shaping function with an impulses response pMc,T.
Mixer 134 is operable to mix waveform signal 166 with signal 168 to assign it another appropriate carrier frequency slot for transmitting. For transmitting source 104, signal 168 is represented as ej(2πfMct+0Mc)/√Mc.
Adder 136 is operable to add output signals from different transmitting sources and provide a composite signal 172 to HPA 106. In FIG. 1, adder 136 is shown to add output signal 164 from transmitting source 102 and output signal 170 from transmitting source 104, however, there may be more output signals from other carriers going to adder 136 to generate composite signal 172. Composite signal 172 at the transmitter output can be described in complex form as:
                                                        s              c                        ⁡                          (              t              )                                =                                    ∑                              m                =                1                                            M                c                                      ⁢                                                  ⁢                                          1                                                      M                    c                                                              ·                                                s                  m                                ⁡                                  (                  t                  )                                            ·                              ⅇ                                  j                  ⁡                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          m                                                ⁢                        t                                            +                                              θ                        m                                                              )                                                                                      ,                            (        1        )            where individual waveform sm(t), as represented by waveform signal 160 (for m=1) or waveform signal 166 (for m=Mc), are digitally modulated, and given by:
                                                        s              m                        ⁡                          (              t              )                                =                                    ∑                              k                =                                  -                  ∞                                            ∞                        ⁢                                                  ⁢                                          a                                  m                  ,                  k                                            ·                                                p                                      m                    ,                    T                                                  ⁡                                  (                                      t                    -                                          kT                      s                                        -                                                                  ε                        m                                            ⁢                                              T                        s                                                                              )                                                                    ,                            (        2        )            {εm, θm} represents normalized difference in signal arrival time and carrier phase, respectively, and fm is the mth center frequency. In equation (2), pm,T(t) is the impulse response of transmit filter 120 (for m=1). It more generally models the cascade of pulse shaping filter and on-board input multiplexing filter.
For better utilization of bandwidth, the case of uniform spacing in frequency, say Δf, is considered, alternatively
                                                        f              m                        =                                                            (                                      m                    -                                                                                            M                          c                                                +                        1                                            2                                                        )                                ·                Δ                            ⁢                                                          ⁢              f                                ;                      m            =            1                          ,        2        ,        …        ⁢                                  ,                              M            c                    .                                    (        3        )            However, the analysis presented here is applicable to any other frequency plan.
HPA 106 is operable to receive composite signal 172 and provide an amplified nonlinear composite signal 174, represented by sNL(t), to be transmitted through a communication link, for example, a satellite system. HPA 106 is modeled as a nonlinear memory-less device, whose input-output relationship can be expressed as a power series:
                                                        s              NL                        ⁡                          (              t              )                                =                                    ∑                              l                =                0                            ∞                        ⁢                                          γ                                  (                                                            2                      ⁢                      l                                        +                    1                                    )                                            ·                                                [                                                            s                      c                                        ⁡                                          (                      t                      )                                                        ]                                                  l                  +                  1                                            ·                                                [                                                            s                      c                      *                                        ⁡                                          (                      t                      )                                                        ]                                l                                                    ,                            (        4        )            where {γ(2l+1)} is a set of complex valued coefficients that accounts for Amplitude-to-Amplitude Modulation (AM/AM) and Amplitude-to-Phase Modulation (AM/PM) distortions. The absence of even order product terms in equation (4) is due to the bandpass nature of the nonlinearity which produces contribution that is outside the frequency band of interest.
Adder 138 is modeled to add amplified nonlinear composite signal 174 to AWGN, represented by n(t), with single sided power spectral density of N0 (Watts/Hz) represented by a signal 176 such that a receiver front end input signal 178, represented by r(t), can be expressed as:
mr(t)=sNL(t)+n(t).  (5)
Each receiver front end includes a receive filter to frequency translate each carrier to baseband and to apply a filtering operation with impulse response pm,R(t) so that the noise is rejected in the non-signal band. For receiver front end 108, mixer 140 is operable to mix received signal 178 with a signal 180 to adjust the amplitude and also remove the frequency component added by transmitting source 102. Signal 180 can be represented as √Mce−j(2πf1t+01).
Receive filter 142 is operable to apply a filtering operation with impulse response pl,R(t) on a waveform signal 182 such that the noise is rejected in the non-signal band. The input-output relationship of the mth receive filter bank can be expressed as:
                                          x            m                    ⁡                      (            t            )                          =                              ∫                          -              ∞                        ∞                    ⁢                                    r              ⁡                              (                                  t                  -                  τ                                )                                      ⁢                                          M                c                                      ⁢                                          ⅇ                                  -                                      j                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                                                    f                              m                                                        ⁡                                                          (                                                              t                                -                                τ                                                            )                                                                                                      +                                                  θ                          m                                                                    )                                                                                  ·                                                p                                      m                    ,                    R                                                  ⁡                                  (                  τ                  )                                                      ⁢                                                  ⁢                                          ⅆ                τ                            .                                                          (        6        )            
More generally, receive filter pm,R(t) models the cascade of a matched filter and an on board output multiplexing filter, collectively referred here as a receive filter bank. Each of receiver front end 108 and 110 is sometimes referred as a branch of receive filter bank in this application. Further, outputs of the receive filter bank are sampled at the symbol rate to produce xm((n+εm)Ts); m=1, 2, . . . Mc. For receiver front end 108, an output waveform 184 of receive filter 142 is sampled at the symbol rate by sampling switch 144 to produce a receive sample signal 186, represented by x1((n+ε1)Ts).
Operation of receiver front end 110 is similar to 108, where an output waveform 190 of receive filter 148 is sampled at the symbol rate by sampling switch 150 to produce a receive sample signal 194, represented by xMc((n+εMc)Ts).
As discussed above with reference to FIG. 1, due to multiple carriers sharing same transponder HPA 106, x1 . . . xMc contain high levels of interference or IMD as a result of the nonlinear impact, filtering and the proximity of the signals. Since the composite of these high-order modulation carriers suffers from large amplitude fluctuations, severe level of IMD among carriers can be generated causing unacceptable performance degradation.
What is needed is a system and method to provide nonlinear compensation for IMD in multicarrier communication systems, where multiple carriers share the same transponder HPA.